Time doesn't slow down when you approach the speed of light and the theory we're using to describe much of the universe is based on a bad premise, that the speed of light is constant.
I don't care that I'm not as smart as einstein or that a lot of complex theories i also don't fully understand are validated by special and general relativity. I, an everyman, know better.
Time doesn't slow down when you approach the speed of light
Correct, but only from your perspective. To other people you've slowed down, but from where you're sitting (or careening through the cosmos at the universal speed limit) everything happens just as fast as it normally does.
the theory we're using to describe much of the universe is based on a bad premise, that the speed of light is constant.
Quasi-correct. "The speed of light" as we think of it in physics is actually the speed of information, which dictates how quickly changes can propagate outwards (or put another way: how quickly you can know about something happening elsewhere). We refer to it as the speed of light because photons move at that speed in a vacuum due to having no mass and thus moving at the fastest possible speed, but things like gravitational waves also propagate at that same speed and have nothing to do with EM radiation. However, the speed of information doesn't change; it's a hard natural law with no known exceptions.
Physics in general is cheating for this thread though, because the answer to what makes stuff happen as we understand it is a giant metaphorical mass of "I 'unno." The Standard Model, relativity, quantum mechanics, string theory, etc all have giant gaping holes in them that other models can often fill, but cannot be properly combined in any way that we've tried so far. They're still correct enough to base your entire life around without any worries, but there's always that last 0.01% that amounts to the margins of old maps reading "Here There Be Dragons".
But there is a theory that if light doesn't have mass its speed should theoretically be infinite and light is just limited by the universal speed limit, some other constant or perhaps even variable that we don't fully understand.
Just piling onto this I really hate how it's always portrayed as if ftl would somehow break causality. I cannot for the life of me figure out any way in which something travelling faster than light would do that. Travelling faster than sound doesn't break the air eithe (well it sort of does but the air is still there working as air once the sonic boom has passed it)r.
Bit of a tangent but I get the feeling a lot of scientists are stuck revering the old geniuses a bit too much. Einsteins formula is basically taken as gospel, to suggest it might be inaccurate is seemingly treated as heresy and I don't think that's a good thing.
Newton's theory of gravity was also revered as undenoable fact but lo and behold it was severely inaccurate. What makes these people believe it's any different with Einstein and co? (arguably this could be down to the media distorting sentiment among scientists but that only improves things marginally)
Newtons laws actually do an amazingly good job of describing motion in the realms of physics we typically interact with. Newtons laws aren't wrong, for things like making an airplane fly and boats float, or things like throwing a ball/shooting an arrow/shooting a bullet, they're just incomplete when you look at the "extremes" like inner planetary orbits. The main reason Einstein is so revered is because he was able to develop a theory and equations that do accurately predict what had been observed.
Almost certainly Einsteins theory is similarly incomplete, we just have to find the extremes where its predictions don't agree with experiment and then understand what the experiment results actually mean and what could cause them.
One thing to always remember is that all these laws and theories and equations are just ways to model and predict the reality we experience.
All models are wrong. Some models are useful.
Newton's theory of gravity ... severely inaccurate.
Except it's not - it's accurate enough within certain limits to still be useful today. It's only inaccurate in extreme cases. Relativity is more accurate, sure, but outside of the extremes, it's more complex than Newton's and not worth the extra trouble.
The "speed of light" is represented by the letter c, because it's actually not the speed of light, it's the speed of causality. We can't observe light going faster than that limit, because we'd be seeing the effect before the cause. In short, FTL travel doesn't break causality as a side effect, you'd have to break causality to do any FTL travel.